Algebra Examples

$- 8 x^{2} \sqrt{180} + 9 x \sqrt{5 x^{2}}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $180$ as $6^{2} \cdot 5$ .

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Step 1.1.1

Factor $36$ out of $180$ .

$- 8 x^{2} \sqrt{36 (5)} + 9 x \sqrt{5 x^{2}}$

Step 1.1.2

Rewrite $36$ as $6^{2}$ .

$- 8 x^{2} \sqrt{6^{2} \cdot 5} + 9 x \sqrt{5 x^{2}}$

Step 1.2

Pull terms out from under the radical.

$- 8 x^{2} (6 \sqrt{5}) + 9 x \sqrt{5 x^{2}}$

Step 1.3

Multiply $6$ by $- 8$ .

$- 48 x^{2} \sqrt{5} + 9 x \sqrt{5 x^{2}}$

Step 1.4

Reorder $5$ and $x^{2}$ .

$- 48 x^{2} \sqrt{5} + 9 x \sqrt{x^{2} \cdot 5}$

Step 1.5

Pull terms out from under the radical.

$- 48 x^{2} \sqrt{5} + 9 x (x \sqrt{5})$

Step 1.6

Multiply $x$ by $x$ by adding the exponents.

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Step 1.6.1

Move $x$ .

$- 48 x^{2} \sqrt{5} + 9 (x \cdot x) \sqrt{5}$

Step 1.6.2

Multiply $x$ by $x$ .

$- 48 x^{2} \sqrt{5} + 9 x^{2} \sqrt{5}$

Step 2

Add $- 48 x^{2} \sqrt{5}$ and $9 x^{2} \sqrt{5}$ .

$- 39 x^{2} \sqrt{5}$